A comprehensive approach to portfolio optimization based on modern mathematical modeling methods

 In this study, an integrated approach to portfolio optimization is presented, combining modern time series forecasting methods and flexible settings for portfolio optimization. In conditions of high volatility in the digital asset market, traditional models such as Markowitz and CAPM lose their effectiveness without accurate return forecasts, as they do not account for dynamically changing market conditions. In this work, an approach is proposed that includes the adaptive selection of forecasting models for each asset and the optimization of portfolio weights based on forecast data. For asset price forecasting, ARIMA, Chronos Forecasting, GMDH, and LSTM models are employed, which allows various aspects of market dynamics to be taken into account. Based on the forecasts, a covariance matrix of returns is calculated and portfolio optimization is performed considering different strategies: allowing short positions, risk minimization, and achieving a predetermined level of return. The approach was tested on data from yfinance with various parameter configurations, including the number of assets, forecast horizon, and data scaling approaches. The experimental results show that the proposed approach yields an average realized portfolio return of 55.2%, with the proportion of portfolios achieving positive returns reaching 83.3%. Using the median as the scaling strategy increases the average return to 66.9%, with 92.6% of the portfolios being successful. This approach serves as a tool for investors, allowing strategies to be adapted to changing market conditions and enhancing the efficiency of digital asset portfolio management. Furthermore, the proposed approach demonstrates a high degree of flexibility due to the ability to adjust various optimization parameters. For example, varying the forecast horizon allows both short-term and long-term market trends to be taken into account, while the choice of scaling strategy influences prediction accuracy. Portfolio optimization is carried out considering various metrics, making the approach applicable to both conservative and aggressive investment strategies. Further research may include expanding the set of forecasting models, integrating alternative optimization strategies, and applying the proposed approach to traditional financial markets. This would enhance forecasting accuracy and the effectiveness of investment management under conditions of high uncertainty and volatility in digital assets.